I have difficulties understanding an easy method to find the generalized eigenvectors of a nilpotent matrix.
For example, for the matrix A= 1st : 1 0 0
2nd; -1 2 0
3rd: 1 1 2
The first eigenvalue is 1, and the other is 2 with multiplicity 2.
I know how to find the first eigenvector for eigenvalue 1 which is v1= (1,1, -2)^T, but I got difficulty to find the two other ones. The book gives for v2= (0,0, 1)^T, and for V3, he added to use formula (A-2I)^2 v =0 to find v3 to be v3= (0,1,0)^T.
I tried to follow but I cannot find how to get v3.
( I have the complete solution for the IVP, all I need are the eigenvectors).
Please explain this to me!© BrainMass Inc. brainmass.com October 10, 2019, 5:44 am ad1c9bdddf
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The solution is attached below in two files. The files are identical in content, only differ in format. The first is in MS Word format, while the other is in Adobe pdf format. Therefore you can choose the format that is most suitable to you.
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If an eigenvalue has multiplicity m there might not be a set of linearly independent ...
The expert determines how to find generalized eigenvectors.